Question

Let A be a nonsingular square matrix of order 3 × 3. Then is equal to A. B. C. D.

Answer 1

We know that,

( adjA )A=| A |I =| A |[ 1 0 0 0 1 0 0 0 1 ] =[ | A | 0 0 0 | A | 0 0 0 | A | ]

Further simplify,

| ( adjA )A |=| | A | 0 0 0 | A | 0 0 0 | A | | | adjA || A |= | A | 3 | 1 0 0 0 1 0 0 0 1 | | adjA || A |= | A | 3 I | adjA |= | A | 2

Hence, option (B) is the correct.